All Propositions Are True
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after 1 vote the winner is...
ElliottR
Voting Style:  Open  Point System:  7 Point  
Started:  4/30/2017  Category:  Philosophy  
Updated:  3 years ago  Status:  Post Voting Period  
Viewed:  1,362 times  Debate No:  102307 
Debate Rounds (3)
Comments (6)
Votes (1)
Consider the proposition p = "A rectangle is a square." Since some rectangles are squares, a rectangle is a square. Thus, p is true. Since some rectangles are not squares, a rectangle is not a square. Thus, p is not true. So by Conjunction Introduction, p is true and p is not true. But that is a contradiction. Since every proposition follows from a contradiction by the Principle of Explosion, the proposition "all propositions are true" is true. Therefore, all propositions are true.
The proposition p is invalid and essentially meaningless as it does not make any reference to the circumstance under which it is true. i.e. it has no context. You may as well say p = "The sky is blue". Isolated from its context, this too would also be invalid and meaningless. The valid statement would be p = "The sky is sometimes blue in the daytime" (i.e it's grey when it's raining, black in the night time etc..) Your very next sentence however, does give the correct context though. i.e Only "some rectangles are squares" So for the proposition to be valid it must become p = "Some rectangles are squares". I'm afraid the rest of your argument falls apart very quickly after this. 

p is true if and only if a rectangle is a square. More information isn't necessary. Propositions of a similar form seem prevalent.
The word "is" implies the present time. "Larson Geometry" (2012) p. 509, "Geometry" (2012) by Burger, Chard, et al. p. 403, and "Geometry" (2012) by Carter, Cuevas, et al. p. 403 all state the following proposition as a theorem. If a quadrilateral is a parallelogram, then its opposite sides are congruent. The hypothesis of the conditional statement is a proposition with a form similar to "A rectangle is a square." "Larson Geometry" p. 8687, "Geometry," Burger, et al. p. 81, and "Geometry," Carter, et al. p. 107 use symbolic notation to express conditional statements. This use suggests the hypothesis "A quadrilateral is a parallelogram" is a proposition, which further suggests "A rectangle is a square" is a proposition. "Some rectangles are squares" does not have the same meaning as p does. The former is always true, but the latter is sometimes false.
Your first line  "p is true if and only if a rectangle is a square" Therefore, p is false if and only if a rectangle is not a square. Hence, there is no contradiction. p cannot be both true and false at the same time and under the same conditions. i.e. within the same context. 

You could argue that "A rectangle is a square" from the second sentence of my argument in Round 1 is not the same proposition as "A rectangle is a square" from the fourth sentence because the rectangle being referred to in the second sentence isn't the same rectangle being referred to in the fourth sentence. While I agree the rectangles aren't the same, p does not require them to be the same. The three textbooks I cited use propositions such as "A quadrilateral is a parallelogram" in a manner such that they apply to each member of the subject's type. Likewise, I am using "A rectangle is a square" in a manner such that the proposition applies to each rectangle. "A rectangle is a square" is sometimes true.
You could argue it's more likely presenting propositions in this manner is wrong than it's likely all propositions are true. While an honorable argument, this prevailing manner of presentation has withstood the test of time and has survived every criticism against it.
You seem to be broadening the debate into how best to present your proposition. I'll just stick to your base argument. Your primary argument is that p is true and false at the same time and under the same conditions. Your argument relies on a contradiction. Unfortunately, this goes against a fundamental law of existence. Aristotle's Law of Identity. i.e. A is A. This means, existence cannot contain contradictions. No valid or meaningful statement can be made if Ideas, Propositions, Knowledge are looked at in isolation. i.e. taken out of context. In other words, "You can't have your cake and eat it too" 
1 votes has been placed for this debate.
Vote Placed by Jonbonbon 3 years ago
holla1755  ElliottR  Tied  

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Reasons for voting decision: Pro proposed a blatant contradiction could be considered truth. It was a weird path of thought that went from some rectangles being squares to saying that all rectangles are squares to affirm a proposition. Pro even recognizes this contradiction and fixes it by essentially saying reality must be wrong about this one, because unless we affirm this proposition we have a contradiction that is also true. Con pointed out that according to the law of identity a thing that exists cannot contain contradictions, and he also pointed out that con needed to adjust his equation to make it correct. The proposition is the central argument in the debate, and con showed that it should be "some rectangles are squares" not "a rectangle is a square" because the latter option is not always a true statement.
>Reported vote: Grayneer// Mod action: Removed<
3 points to Con (Arguments). Reasons for voting decision: "Since some rectangles are squares, a rectangle is a square" classic equivocation good meme tho
[*Reason for removal*] The voter is required to specifically assess arguments made by both sides. Merely quoting a single line and stating the voter"s own views on it is not sufficient.
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You commit the fallacy of equivocation. A particular rectangle, X, is not the same as the set of all possible rectangles. Just because some rectangles are squares, doesn't mean that every rectangle is a square. And , X can only be either square or not square. Can you refer to a square which is not a square? It is only true insofar as it is an absurd conception, affirmed because we can think of it. It may be true that I can think that X is a square and not a square, but this holds no sort of reference or external reality.